English

Invariant states and rates of Convergence for a critical fluid model of a processor sharing queue

Probability 2009-09-29 v1

Abstract

This paper contains an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue. Specifically, we consider the behavior of solutions of critical fluid models as time approaches \infty. The main theorems of the paper provide sufficient conditions for a fluid model solution to converge to an invariant state and, under slightly more restrictive assumptions, provide a rate of convergence. These results are used in a related work by Gromoll for establishing a heavy traffic diffusion approximation for a processor sharing queue.

Keywords

Cite

@article{arxiv.math/0405289,
  title  = {Invariant states and rates of Convergence for a critical fluid model of a processor sharing queue},
  author = {Amber L. Puha and Ruth J. Williams},
  journal= {arXiv preprint arXiv:math/0405289},
  year   = {2009}
}